Day 14 – RIGID MOTION AND CONGRUENCE

Introduction When someone’s face is reflected by a plane mirror, theoretically, its size and shape remains the same. Similarly if an object is subjected to a rigid motion its shape and size does not change. If two objects have the same size and shape, they are said to be congruent.

Vocabulary Congruence – Two figures are said to be congruent if there is one or more rigid motions that can map one figure onto the other.

Given two figures which have the same size and shape there is always one or more rigid motions that will make one object map on the other regardless of their orientation and distance between them. In some cases, one rigid motion will make the figures map onto each other, but in other cases, we need to apply a combination of more than one rigid motions for them to map onto each other. If one or more rigid motions are found that will map one figure onto the other then the two figures are said to be congruent.

Therefore, given two figure, we need to find a rigid motion that will map one figure onto the other to find whether they are congruent or not. If there is rigid motion(s) exists, then the two figures are congruent. The symbol of congruence is ≅ .

Example. Is ∆𝐴𝐵𝐶 ≅ ∆𝑋𝑌𝑍 ? A B C X Y Z

Solution By definition of congruence, we need to find a rigid motion that will map one triangle onto the other. The rigid motion is glide reflection. Reflect ∆𝐴𝐵𝐶 about a horizontal line that is half way between the two triangles then move the image to the right to coincide with ∆𝑋𝑌𝑍 making ∆𝐴𝐵𝐶 ≅ ∆𝑋𝑌𝑍.

homework 1. Are two hexagons below congruent to each other? Explain.

Answers to homework We need to find a rigid motion that will map one hexagon onto the other. The rigid motion is translation. The first hexagon can be moved to the right until it coincides with the second hexagon. Thus the Two hexagons are congruent.

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